Fa\a di Bruno Hopf algebras

H Figueroa, JM Gracia-Bondia, JC Varilly - arXiv preprint math/0508337, 2005 - arxiv.org
arXiv preprint math/0508337, 2005arxiv.org
This is a short review on the Fa\a di Bruno formulas, and some Hopf algebras associated to
them. These allow, among several other things, a short proof of the Lie-Scheffers theorem,
and relating the Lagrange inversion formulas with antipodes. The link of Fa\a di Bruno
formulas with the theory of set partitions is developed in some detail.
This is a short review on the Fa\`a di Bruno formulas, and some Hopf algebras associated to them. These allow, among several other things, a short proof of the Lie-Scheffers theorem, and relating the Lagrange inversion formulas with antipodes. The link of Fa\`a di Bruno formulas with the theory of set partitions is developed in some detail.
arxiv.org